A mathematical model for transmission dynamics of COVID-19 infection

Abstract

In this paper, a mathematical model of COVID-19 has been proposed to study the transmission dynamics of infection by taking into account the role of symptomatic and asymptomatic infected individuals. The model has also considered the effect of non-pharmaceutical interventions (NPIs) in controlling the spread of virus. The basic reproduction number (R) has been computed and the analysis shows that for R< 1 , the disease-free state becomes globally stable. The conditions of existence and stability for two other equilibrium states have been obtained. Transcritical bifurcation occurs when basic reproduction number is one (i.e. R= 1). It is found that when asymptomatic cases get increased, infection will persist in the population. However, when symptomatic cases get increased as compared to asymptomatic ones, the endemic state will become unstable and infection may eradicate from the population. Increasing NPIs decrease the basic reproduction number and hence, the epidemic can be controlled. As the COVID-19 transmission is subject to environmental fluctuations, the effect of white noise has been considered in the deterministic model. The stochastic differential equation model has been solved numerically by using the Euler-Maruyama method. The stochastic model gives large fluctuations around the respective deterministic solutions. The model has been fitted by using the COVID-19 data of three waves of India. A good match is obtained between the actual data and the predicted trajectories of the model in all three waves of COVID-19. The findings of this model may assist policymakers and healthcare professionals in implementing the most effective measures to prevent the transmission of COVID-19 in different settings.